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It is shown that there are 41 types of multivectors representing physical quantities in non-relativistic physics in arbitrary dimensions within the formalism of Clifford algebra. The classification is based on the action of three symmetry operations on a general multivector: spatial inversion, 1 , time-reversal, 1′, and a third that is introduced here, namely wedge reversion, 1 † . It is shown that the traits of `axiality' and `chirality' are not good bases for extending the classification of multivectors into arbitrary dimensions, and that introducing 1 † would allow for such a classification. Since physical properties are typically expressed as tensors, and tensors can be expressed as multivectors, this classification also indirectly classifies tensors. Examples of these multivector types from non-relativistic physics are presented.
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ProtoTEx: Explaining Model Decisions with Prototype Tensors
We present ProtoTEx, a novel white-box NLP classification architecture based on prototype networks (Li et al., 2018). ProtoTEx faithfully explains model decisions based on prototype tensors that encode latent clusters of training examples. At inference time, classification decisions are based on the distances between the input text and the prototype tensors, explained via the training examples most similar to the most influential prototypes. We also describe a novel interleaved training algorithm that effectively handles classes characterized by ProtoTEx indicative features. On a propaganda detection task, ProtoTEx accuracy matches BART-large and exceeds BERTlarge with the added benefit of providing faithful explanations. A user study also shows that prototype-based explanations help non-experts to better recognize propaganda in online news.
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- PAR ID:
- 10350188
- Date Published:
- Journal Name:
- Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics
- Page Range / eLocation ID:
- 2986 to 2997
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.18653/v1/2022.acl-long.213
